Analyzing Structure–Activity Variations for Mn–Carbonyl Complexes in the Reduction of CO2 to CO

Contemporary electrocatalysts for the reduction of CO2 often suffer from low stability, activity, and selectivity, or a combination thereof. Mn–carbonyl complexes represent a promising class of molecular electrocatalysts for the reduction of CO2 to CO as they are able to promote this reaction at relatively mild overpotentials, whereby rare-earth metals are not required. The electronic and geometric structure of the reaction center of these molecular electrocatalysts is precisely known and can be tuned via ligand modifications. However, ligand characteristics that are required to achieve high catalytic turnover at minimal overpotential remain unclear. We consider 55 Mn–carbonyl complexes, which have previously been synthesized and characterized experimentally. Four intermediates were identified that are common across all catalytic mechanisms proposed for Mn–carbonyl complexes, and their structures were used to calculate descriptors for each of the 55 Mn–carbonyl complexes. These electronic-structure-based descriptors encompass the binding energies, the highest occupied and lowest unoccupied molecular orbitals, and partial charges. Trends in turnover frequency and overpotential with these descriptors were analyzed to afford meaningful physical insights into what ligand characteristics lead to good catalytic performance, and how this is affected by the reaction conditions. These insights can be expected to significantly contribute to the rational design of more active Mn–carbonyl electrocatalysts.


Overpotential from Experimental Cyclic Voltammograms
The /2 values for each catalytic wave ( Figure S1a) were determined based on the local maxima in the first derivative plots in Figure S1b. This is a method similar to the one used previously to evaluate half-wave potentials for molecular cobalt complexes for H2 evolution. 1 When multiple local maxima are present, as is the case in Figure S1, the maximum associated with greater catalytic enhancement (usually the reduction-first pathway) is chosen as the /2 of the catalyst. While there may be some ambiguity as to how accurately /2 represents the true half-wave potential of the catalyst, it is a consistent method for

Foot of the Wave (FOTW) Analysis for Calculating TOFmax from Experimental Cyclic Voltammograms
Calculating the TOFmax for Mn-carbonyl catalysts from different kinetic studies is not trivial. In some cases, catalyst TOFmax, TOFs at certain potentials, or catalytic-current enhancements have already been reported, albeit that often differences in how these figures are calculated make it challenging to use them for accurate comparisons. Furthermore, in a majority of the 55 Mn-carbonyl catalysts considered here, no kinetic figures are reported, and only the cyclic voltammogram itself is given as a measure of catalyst performance. Therefore, only the shape of the cyclic voltammogram can be used to calculate the TOFmax.
To get an understanding of how the shape of a cyclic voltammogram can yield kinetic information about a catalyst, we derive the expression for the catalytic current following a simplified reaction scheme.
The reduction of CO2 to CO by Mn-carbonyl catalysts can be described generally by Equations S2-S4. It should be noted here that several electron transfers and chemical steps are omitted for simplicity, and the full mechanism is described in more detail in Figure 1.
During the catalytic reaction, Q is only found between the surface (x = 0) in the reaction-diffusion layer (0 < x < ), which has a thickness . 12 In the reaction-diffusion layer, the concentration profile of Q can be expressed by the differential equation in Equation S9 assuming all mass transport is driven by diffusion.
The concentration profile of Q is affected by diffusion of Q from the electrode surface, where P gains electrons to form Q, and by consumption of Q by reaction with molecules of CO2 that are near the surface.

Equation S10
gives the general solution using these boundary conditions. S5 ( ) = ,0 (− √ ) (S10) Now that the concentration profile of Q is known, the current flowing through the electrode surface can be related to the concentration gradient of Q. Equation S11 expresses the current density at the electrode surface (x = 0) in terms of the fluxes of P and Q. 10 By substituting Equation S10 for ( ), Equation S12 is obtained.
In Equation S12, A is the electrode surface area, F is the Faraday constant, and D is the diffusion coefficient of P and Q. Using the Nernst equation to express the concentration of Q as a function of potential (Equation S8), the current can be expressed instead as a function of total catalyst concentration, 0 (Equation S13).
Adhering to the assumptions described above, Equation S13 should exactly define the currentpotential relationship of the experimental cyclic voltammograms under purely kinetic conditions. This gives rise to a sigmoid shape, where at sufficiently positive potentials = 0, and at sufficiently negative potentials = . To evaluate kinetic parameters and gain mechanistic insight of Mn-carbonyl catalysts, catalytic-plateau-current analysis is most often used in practice, because diffusion coefficients and electrochemically active surface areas are unknown. The catalytic plateau current is that current, where at sufficiently negative potentials all catalyst molecules are in the active state; it is also the plateau of the sigmoid response. For an electrochemical reduction followed by an irreversible chemical step (EC' mechanism), the plateau of the catalytic current is given by Equation S14. 13 = 0 √ √ (S14) In this equation, F is the Faraday constant, A is the electrochemically active surface area, D is the diffusion coefficient of catalyst P, 0 is the total concentration of catalyst P in solution, and TOFmax is the S6 maximum turnover frequency, i.e., the observed rate constant. In practice, can be easily determined from the plateau current of an ideal S-shaped CV curve.
The plateau current is often normalized by the current under inert conditions. Under inert conditions, the diffusion coefficients and electrochemically active surface area should be the same as when the substrate (here: CO2) is introduced. Dividing by the peak current in the absence of substrate, , is useful because it enables the evaluation of TOFmax without needing to know the electrochemically active surface area and diffusion coefficients. 13 Equation S15 gives an expression for assuming that the electron transfer between P and Q is Nernstian, while Equation S16 gives an expression for the normalized plateau current.
In these equations, is the scan rate that measures how fast the voltage is swept up and down in the cyclic voltammogram. While n describes the number of electrons needed to convert one molecule of substrate into one molecule of product in the catalytic reaction, describes the number of electrons transferred per unit catalyst in the non-catalytic response.
In practice, the TOFmax of a catalyst can be calculated with just two measurements: (1) The plateau current from the catalytic cyclic voltammogram, and (2) the peak current in the non-catalytic cyclic voltammogram. However, plateau-current analysis is only applicable to S-shaped CV curves where the reverse scan exactly overlaps with the forward scan. This means that catalysis is purely limited by kinetics and there is mass-transport limits caused by substrate consumption. 14 The plateau current must also be independent of the scan rate for the TOFmax calculated from this method to be valid. These strict conditions are rarely met for molecular catalysts. Often, apparent rate constants and TOFs will be reported from imperfectly shaped cyclic voltammograms, or the kinetics are discussed only qualitatively using the ratio of peak current in the presence of substrate to the peak current in the absence of substrate.
The presence of side reactions and substrate depletion distort the shape of the cyclic voltammogram, making it harder to estimate kinetic parameters. FOTW analysis is a technique that allows determining the TOFmax of a molecular catalyst from cyclic-voltammogram curves without requiring a kinetically limiting regime with a well-defined plateau current. This makes it particularly useful for the S7 purpose of consistently evaluating activity metrics across multiple Mn-based molecular catalysts for the reduction of CO2. The FOTW method has been described in detail for two-electron-transfer processes, 5,[15][16][17][18] and has been previously used to determine rate constants for the electrochemical reduction of CO2 promoted by molecular Mn-carbonyl catalysts. [19][20][21] At the "foot" of the catalytic cyclic voltammogram, i.e., at low overpotentials, substrate depletion and other side phenomena are less likely to occur. Using data near the foot of the wave and extrapolating Equation S13 to higher potentials allows for a more accurate determination of TOFmax. More importantly, this allows for consistent method of calculating TOFmax for catalysts that have been reported in the literature without relying on individualized kinetic analysis that may be absent.
To evaluate TOFmax for all 55 Mn-carbonyl catalysts considered here, cyclic voltammograms were mined from individual papers and normalized according to peak current. Two cyclic voltammograms were captured for each catalyst from the publication using DataThief. 22 DataThief is a program that generates data points from images of graphs, which can then be re-plotted and used for further analysis. One cyclic voltammogram shows the current as a function of potential under catalytic conditions, i.e., in the presence of CO2 and a proton donor. The second cyclic voltammogram shows the redox behavior of the catalyst under an inert atmosphere (Argon or N2), and whose peak current is used to normalize the catalytic current.
Both cyclic voltammograms should be performed using the same scan rate and the same concentration of catalyst. The catalytic current is then normalized by the peak current, and the expected functional form (for a kinetically limiting regime) is given in Equation S17.
Here, z is the number of electrons transferred per catalyst in the non-catalytic response (1 or 2), while n is the number of electrons required for catalytic turnover (2), and is the peak of the non-catalytic reduction wave under inert atmosphere.
The ideal S-shaped curve has the functional form (1 + exp ( ( − /2 ))) , the slope (m) of the corresponding line can be used to determine the maximum turnover frequency, which is given by Equation S18.
Deviations from the ideal behavior will appear as nonlinearities far from the FOTW, when | | ≫ | /2 |. Side-phenomena will be minimized at potentials near /2 , and the slope near /2 will give information about the kinetics.  Figure S2 represents the extension of Figure S1 to calculate TOFmax using FOTW analysis. The catalytic half-wave potential /2 = -2.08 V corresponds to a value of 0.5 in Figure S2b. Near the half-S9 wave potential, the FOTW plot is linear. At very low potentials, there are deviations from nonlinearity that arise from an overlap of another wave at lower overpotentials. At high potentials, there are deviations from linearity as substrate depletion results in a peak of the current. The slope of the red dashed line in Figure   S2b is calculated using a linear fit from x = 0.25 to x = 0.70 and Equation S18 is used to calculate TOFmax.

Relative Uncertainty from FOTW Analysis
The relative uncertainty in TOFmax between different Mn-carbonyl catalysts was calculated to assess the confidence of values calculated using FOTW analysis. To assess the uncertainty in the TOFmax determined from the FOTW analysis, the difference between the slope in the strictly linear region and the slope at low values of (i/ip) in Figure S3b is examined. If the slope at low values of (i/ip) is higher (lower) than in the strictly linear region, the catalysis is faster (slower) at the FOTW than expected. In these cases, it is likely that the wave shape in Figure S3a is a result of a superposition of several waves, which may correspond to current from different mechanisms or side reactions with different onset potentials. FOTW analysis assumes that peaks corresponding to redox events are well-separated, but this requirement is not strictly met in all cases. The peak overlap leads to an uncertainty in the TOFmax extracted from the linear region using FOTW analysis. To quantify the impact of these side phenomena in the cyclic voltammograms, the magnitude of the area above or below the ideal linear FOTW region is measured in the region x = 0 to x = 0.25 (pink shaded region between the forward trace of cyclic voltammogram (black line) and the pink dashed in Figure   S3b). The greater this area is, the more the FOTW region is overshadowed by additional redox events that are not related to the catalytic wave at /2 . To give meaning to this area, a line of slope m is constructed that intersects the FOTW pink dashed line at x = 0.25, and that has the same magnitude of area in the pink shaded region (cyan dashed line and cyan shaded in Figure S3b). Finally, Equation S18 is used to calculate a revised TOFmax using the slope of the new cyan dashed line (m). The difference between the revised TOFmax and the TOFmax calculated using the linear region (pink line) gives a relative uncertainty in the TOFmax for a given Mn-carbonyl catalyst. Electron transfer between the Mn-carbonyl catalyst and the substrate (e.g., CO2) becomes so fast that electron transfer from the electrode to the catalyst limits the overall kinetics. 17 The FOTW can be extended to these cases by including an additional term that uses the rate constant of electron transfer between the catalyst and electrode (ks in Scheme 1), which can be derived from the cyclic voltammogram of the catalyst redox behavior under inert conditions; however, these electrode-catalyst rate constants are not reported for any of the Mn-carbonyl catalysts considered here. Instead, the current implementation assumes that electron transfer between electrode and catalyst is infinitely fast, and it should be noted here that this may lead to an underestimation of TOFmax for very active catalysts.

Comparing Reported and Calculated TOFmax Values
The inclusion of a "fudge factor" was considered by fitting a curve to Figure S4 to correct this underestimation. As ks depends on the properties of the catalyst and electrode material, such a universal S12 correction may capture incorrect behavior when extrapolated to other catalysts that are not in Figure S4. In either case, there is a clear positive correlation between TOFmax calculated using FOTW analysis and the reported TOFmax, which is adequate for comparing the underlying trends across a series of these catalysts.

Feature Correlations
Some of the features in Table 2 are strongly correlated to each other. Relationships between each of the features are illustrated using a heatmap of the pairwise-correlation coefficients in Figure S5. The intensity of the color and the size of the squares in Figure S5 quantify the degree to which two features are correlated. ∆ 1 and ∆ 2 are negatively correlated with a Pearson correlation coefficient of -0.75. Generally, a highly negative adsorption energy for CO2, i.e., a strong Mn-CO2 bond, also gives rise to a highly positive energy for dissociation energy for H + with the same Mn-complex (i.e., strong Mn-H bond and high pKa).
This negative correlation describes the adsorbate scaling relation for Manganese with H and C atoms.
Ligand modifications that are designed to stabilize the Mn-CO2 reaction intermediate via intramolecular hydrogen bonding can break this correlation. Another interesting correlation that is present in Figure S5 is between 1 and 2 . These two are almost perfectly correlated (r = 0.99), which means that the LUMO orbitals of the H-bound and CO2-bound Mn intermediates are influenced the same way by any changes in the ligand structure. The energy of the LUMOs of the complexes correlate to the partial charge for a given complex. In general, the LUMOs tend to correlate strongly with each other whereas the HOMOs don't. S13 Figure S5. Heatmap showing pairwise correlations between features in Table 2. The Pearson correlation coefficient is reported for each pairwise correlation if it is greater than 0.75. Red represents a negative correlation, while blue represents a positive correlation. The intensity of the color and the size of the squares quantify how strongly the two features are correlated. Table 2

List of SISSO Models
The top three SISSO models for each data subset are listed in Tables S1-S3. Increasing the feature complexity and removing outliers gives better performing models, as shown in Tables S4-S5 for TOF0.

Full Dataset of 55 Mn-Carbonyl Catalysts
The full dataset containing the ligand identifiers, experimental figures of merit, relative uncertainty, and primary features is given in the table below. The table reads from right to left, and each row continues on the following page with the ligand number corresponding to the ligand structures given in Table 1. All energies are given in kJ/mol. A legend for the table headers is given in Table S6.